## geerky42 one year ago Does Batman Equation really work? And can we "union" relations? (Sorry for long reply.)

1. geerky42

I just happened to discover this question in Math Stack Exchange (MSE): http://math.stackexchange.com/questions/54506/is-this-batman-equation-for-real/54568#54568 Here's the image: |dw:1435886055793:dw| http://i.stack.imgur.com/VYKfg.jpg I tried to graph it on Desmos: https://www.desmos.com/calculator/cscx2zcrlf Graphing each factor separately turns out well, however when I multiply all factors, graph won't appear. I think Desmos just choke on it, so I tried something simple; https://www.desmos.com/calculator/enxuzekis6 Yet it doesn't show anything... So apparently image above is not true. My questions are: $$\Large 1)$$ Is there any way to union relations? By "union," I mean in $$\mathbb R^2$$, if you union $$f(x,y)=0$$ and $$g(x,y)=0$$, then you would have new union relation $$U(x,y)=0$$, which if you graph it, then $$f(x,y)=0$$ and $$g(x,y)=0$$ would both be graphed simultaneously. From image, it's $$U(x,y) = f(x,y)g(x,y)=0$$, but it seems that it is not true. $$\Large 2)$$ Why does no one seem to notice that image is not true in MSE question?

2. anonymous

A relation is a set, so obviously you could union two relations.

3. geerky42

Yeah I know. Not sure what's correct word for that, but let's just stick with "union" By "union," I mean saying if you graph $$f(x,y)=0$$ and $$g(x,y)=0$$, you would see something on xy plane. If we "union" these relations, then we would have new relation $$U(x,y)=0$$, such that if you graph $$U(x,y)$$, then you would see same thing as if you graph $$f(x,y)=0$$ and $$g(x,y)=0$$ separately at the same time.

4. geerky42

From shown image, you just multiply relations, but to me, it doesn't work.

5. just_one_last_goodbye

In my opinion it doesn't work :/ very complex and in testing ur not going to really make a perfect batman sign on the graph xD

6. anonymous

We are such math nerds XD

7. geerky42

For example; saying we have $$f(x,y) = x^2+y^2 -1= 0$$ and $$g(x,y) = (x+2)^2+y^2-1=0$$ Then $$U(x,y)$$ would graph this:|dw:1435887037303:dw| Exactly what is $$U(x,y)$$? and how can I "combine" f(x,y) and g(x,y) to form U(x,y)?

8. geerky42

Wut now it works. https://www.desmos.com/calculator/uezz1quzdy Now I am confused lol...

9. geerky42

Got something to do with restrictions, I guess. That circles equation above here has no restriction, but Batman Equation does.

10. geerky42

https://www.desmos.com/calculator/enxuzekis6 First relation is restricted to $$x>1$$ Second relation is restricted to $$x<1$$ So together they would not appear in graph simply because they would be somewhere in complex. Just like Batman Equation. Is there any way to prevent that? OK I think that's too much to ask lol...

11. geerky42

@iambatman ( ͡° ͜ʖ ͡°)

12. anonymous

Im batman (in husky batman voice) o.o

13. anonymous

Yes, the roots of $$f\cdot g$$ is the union of the roots of $$g$$ and the roots of $$f$$.

14. anonymous

Only exceptions are when you have different domains

15. anonymous

You intersect the domains, then you union the roots in that intersected domain

16. geerky42

OK, I think I asked rather silly and pointless question. But thanks for put in effort for me.

17. nincompoop

Superman > Batman

18. Australopithecus

nincompoop I am afraid you made a mistake, it should be: Superman < Batman

19. UsukiDoll

That's super cool. I wonder if there will be a bunch of equations that can produce the Avengers Logo? When I was taking Calculus III there were some equations in polar coordinates that produced flowers, the number 8, or the infinity symbol.

20. UsukiDoll

Anyway, graphing these equations separately was a good idea. If it was bunched up together, wouldn't something overlap and eventually the Batman Logo will no longer appear?

21. TheSmartOne

@iambatman should know xD

22. anonymous

Haha, I believe it was here I posted something similar long time ago, in any case it seems you've figured out what your problem was? @geerky42 @nincompoop I resent that!

23. ybarrap

FYI - Here is the Batman Equation implemented in Geogebra: $$\href{http:///www.geogebra.org/m/114}{Batman}$$